If tan - - cot - - 2- then the value of tan3 -1tan3 - is

Nbsp;tan θ+1tan^3 nbsp;θ ⇒ nbsp;tan^3 nbsp;θ+1tan^3 nbsp;θ= ( tan θ +1tan θ ) ( tan^2 θ +1tan^2θ 1 ) =2 ( ( tan θ +1tan θ )^2 3 ) =2(4 3) =2 ...

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Standard XII

Mathematics

Intersection

If tan θ + co...

Question

If $t a n θ + c o t θ = 2,$ then the value of $t a n^{3} θ + \frac{1}{t a n^{3} θ}$ is

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Solution

The correct option is C 2
$t a n θ + \frac{1}{t a n^{3} θ}$

$\Rightarrow t a n^{3} θ + \frac{1}{t a n^{3} θ} = (t a n θ + \frac{1}{t a n θ}) (t a n^{2} θ + \frac{1}{t a n^{2} θ} - 1)$

$= 2 ({(t a n θ + \frac{1}{t a n θ})}^{2} - 3)$

= $2 (4 - 3)$

=2

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If tanθ+cotθ=2, then the value of tan3θ+1tan3θ is

The correct option is C 2tanθ+1tan3θ ⇒tan3θ+1tan3θ=(tanθ+1tanθ)(tan2θ+1tan2θ−1) =2((tanθ+1tanθ)2−3) =2(4−3) =2

If $t a n θ + c o t θ = 2,$ then the value of $t a n^{3} θ + \frac{1}{t a n^{3} θ}$ is

The correct option is C 2
$t a n θ + \frac{1}{t a n^{3} θ}$

$\Rightarrow t a n^{3} θ + \frac{1}{t a n^{3} θ} = (t a n θ + \frac{1}{t a n θ}) (t a n^{2} θ + \frac{1}{t a n^{2} θ} - 1)$

$= 2 ({(t a n θ + \frac{1}{t a n θ})}^{2} - 3)$

= $2 (4 - 3)$

=2